Flexible master surgery scheduling: combining optimization and simulation in a rolling horizon approach

Abstract

Operating room managers are facing increasingly complex challenges, namely in complying with waiting time targets before surgery. This paper proposes a framework that combines optimization and simulation to generate dynamic master surgery schedules for a long planning horizon, in which the schedules are optimized by an integer programming model and the demand levels are modelled using the simulation model. The developed approach allows the resulting operating room plan to balance waiting lists as it assigns more time to the specialties with higher demand in terms of time needed to perform all the surgeries in the corresponding waiting lists. The analysis of the results obtained for the proposed flexible rolling horizon approach were proven robust, and were compared to static and flexible long-term approaches, the former not allowing flexibility and the latter using a deterministic update of the demand. Considering throughput, tardiness and waiting time, the flexible rolling horizon approach showed the best results, while the static one had the worst results.

Appendix

1.1 Appendix 1: Overview of the proposed optimization model

Model	Input data	Performed action	Output	Technology
Optimization model	Value of the sets and parameters needed to run the optimization model (see Sect. 3.1)	Solve the optimization model described in Sect. 3.2	Optimization model solution (MSS)	cplex-Java

1.2 Appendix 2: Overview of each component of the proposed simulation approach

Models	Input data	Performed action	Output	Technology
Wait list generation sub model	Patients in the waiting list at the beginning of year b; Patient arrivals in year b-1; Surgical times and LOS for each surgery type	Creation of a demand stream based on the arrivals of year b-1	Waiting list queue: queue of form entities representing patients waiting for surgery and storing all the patients (name, age, address, type, etc..) and surgery attributes (specialty, ICD9CM diagnosis and procedure code, priority class, due date)	Rockwell Arena, VBA
MSS creation sub-model	Waiting list queue data; Forecast of the number of patients that will join the waiting list in the following T days; Optimization model solution	Scan the waiting list queue and the available hospital resources (beds, OR, ICU,etc.) and create the input files with the set and parameters needed by the optimization model; Triggers the optimization model in shell; Reads the optimization model solution and saves the corresponding MSS in an Arena variable	Optimization model input data; Arena matrix variable storing the Optimization output (MSS)	Rockwell Arena, VBA

Models	Input data	Performed action	Output	Technology
MSS implementation sub-model	Arena matrix variable storing the Optimization model’s output; Waiting list queue data; The output of the patient selection heuristic	Triggers the Patient selection heuristic in shell; Reads the solution of the heuristic; Picks the form entities in the Waiting list queue according to the heuristic solution, seizes the resources needed to process them (OR, Beds) for a time sampled from a suitable distribution, records all the time stamps relevant to the patient journey and eventually dismisses the patient	Input data for the patient selection heuristic: Patients waiting for surgery and their attributes, MSS and Scheduled slots duration. Output files recording, for each processed entity, its attributes and the start and end time of each process step it was involved in. For each resource, records its utilization statistics	Rockwell Arena, VBA
Patient selection heuristic	Patients waiting for surgery and their attributes; MSS; Scheduled slot duration	Assign patients in the waiting list to a suitable slot	List of patients to fill in each scheduled slot of the planning horizon	R